Question

A tunnel is 300 feet deep and makes an angle of 30 with the ground .

A.300√3 feet
B.300 feet
C.600 feet
D.100√3 feet

Answer 1

`\boxed{C.\:\: 600\:feet}`

Explanation:

The tunnel, the ground and the depth of the tunnel form a right angle triangle.

The length of the tunnel is the hypotenuse of the right triangle that has been formed.

Let the length of the tunnel be
`m\: feet`.

Using the sine ratio, we obtain;

`\sin(30\degree)=(Opposite)/(Hypotenuse)`

The length of the opposite side is
`300\:feet`

We substitute the given values to obtain;

`\sin(30\degree)=(300)/(m)`

`\Rightarrow (1)/(2)=(300)/(m)`

We cross multiply to obtain;

`m=300*2`

`m=600\:feet`

Therefore the correct answer is C.